Equivariance, BRST and Superspace

TL;DR

This paper explores the mathematical structure of equivariant cohomology in topological field theories using BRST symmetry and superfield formulations, linking to quantization methods in topological Yang-Mills theory.

Contribution

It introduces a superfield formulation of equivariance and connects BRST cohomology with reducible BFV quantization in topological Yang-Mills theory.

Findings

Formulation of equivariance via nilpotent BRST symmetry.

Introduction of a superfield approach to equivariant cohomology.

Connections established between cohomological structures and quantization methods.

Abstract

The structure of equivariant cohomology in non-abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent BRST symmetry, and another nilpotent operator which restricts the BRST cohomology onto the equivariant, or basic sector. A superfield formulation is presented and connections to reducible (BFV) quantization of topological Yang-Mills theory are discussed.